## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2, or (at your option) ## any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: [pval, z] = u_test (x, y [, alt]) ## ## For two samples x and y, perform a Mann-Whitney U-test of the null ## hypothesis PROB(x > y) == 1/2 == PROB(x < y). Under the null, the ## test statistic z approximately follows a standard normal ## distribution. Note that this test is equivalent to the Wilcoxon ## rank-sum test. ## ## With the optional argument string alt, the alternative of interest ## can be selected. ## If alt is "!=" or "<>", the null is tested against the two-sided ## alternative PROB(x > y) != 1/2. ## If alt is ">", the one-sided alternative PROB(x > y) > 1/2 is ## considered, similarly for "<". ## The default is the two-sided case. ## ## pval is the p-value of the test. ## ## If no output argument is given, the p-value of the test is displayed. ## This implementation is still incomplete---for small sample sizes, ## the normal approximation is rather bad ... ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Mann-Whitney U-test function [pval, z] = u_test (x, y, alt) if ((nargin < 2) || (nargin > 3)) usage ("[pval, z] = u_test (x, y [, alt])"); endif if (! (is_vector (x) && is_vector (y))) error ("u_test: both x and y must be vectors"); endif n_x = length (x); n_y = length (y); r = ranks ([reshape (x, 1, n_x), reshape (y, 1, n_y)]); z = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ... / sqrt (n_x * n_y * (n_x + n_y + 1) / 12); cdf = stdnormal_cdf (z); if (nargin == 2) alt = "!="; endif if (! isstr (alt)) error("u_test: alt must be a string"); endif if (strcmp (alt, "!=") || strcmp (alt, "<>")) pval = 2 * min (cdf, 1 - cdf); elseif (strcmp (alt, ">")) pval = cdf; elseif (strcmp (alt, "<")) pval = 1 - cdf; else error (sprintf ("u_test: option %s not recognized", alt)); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction

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